time-frequency analysis of eeg signal processing for

International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064

Index Copernicus Value (2015): 78.96 | Impact Factor (2015): 6.391

Volume 6 Issue 4, April 2017

www.ijsr.net Licensed Under Creative Commons Attribution CC BY

Time-Frequency Analysis of EEG Signal processing

for Artifact Detection

Mst. Jannatul Ferdous*, Md. Sujan Ali

Department of Computer Science and Engineering, Jatiya Kabi Kazi Nazrul Islam University, Mymensingh, Bangladesh

*E-mail: [email protected]

Abstract: EEG is widely used to record the electrical activity of the brain for detecting various kinds of diseases and disorders of the

human brain. EEG signals are contaminated with several unwanted artifacts during EEG recording and these artifacts make the

analysis of EEG signal difficult by hiding some valuable information. Time-frequency representation of electroencephalogram (EEG)

signal provides a source of information that is usually hidden in the Fourier spectrum. The popular methods of short-time Fourier

transform, Hilbert Haung transform and the wavelet transform analysis have limitations in representing close frequencies and dealing

with fast varying instantaneous frequencies and this is often the nature of EEG signal. The synchrosqueezing transform (SST) is a

promising tool to track these resonant frequencies and provide a detailed time-frequency representation. The SST is an extension of the

wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques. This new tool

produces a well-defined time frequency representation allowing the identification of instantaneous frequencies in EEG signals to

highlight individual components. We introduce the SST with applications for EEG signals and produced promising results on synthetic

and real examples.. In this paper, different time-frequency distributions are compared with each other with respect to their time and

frequency resolution. Several examples are given to illustrate the usefulness of time-frequency analysis in electroencephalography.

Keywords: EEG signal, STFT, HHT, WPT, SST, time-frequency representation

1. Introduction

Time-frequency analysis of electroencephalogram (EEG)

during different mental tasks received significant attention.

As EEG is non-stationary, time-frequency analysis is

essential to analyze brain states during different mental

tasks. In the EEG, measured as potential differences on the

human head, variations of the amplitude and frequency of

certain neurological disorders. Therefore time frequency

analysis of the EEG can add valuable information to the

traditional visual interpretation, by providing an image of

the spectral EEG contents varying with time. Further, the

time-frequency information of EEG signal can be used as a

feature for classification in brain-computer interface (BCI)

applications.

Time-frequency representations provide a powerful tool for

the analysis of time series signals. Based on the time-

frequency representation (TFR) of EEG signal. Traditional

time frequency representations, such as the Short-Time

Fourier Transform (STFT) and the Wavelet Transform (WT)

and special representations like Empirical Mode

Decomposition (EMD), have limitations when signal

components are not well separated in the time-frequency

plane. Synchrosqueezing, first introduced in the context of

speech signals [1] has shown to be an alternative to the

EMD method [2] improving spectral resolution.

The recognition, feature extraction and monitoring analysis

and other technologies of variety of physiological signals

including EEG signal has become a hot topic of research in

recent years [3]. All kinds of analysis methods such as

Fourier transformation [4-6], Short Time Fourier

transformation [7-9], wavelet and wavelet package

transformation [10-14], Hilbert-Huang Transformation

(HHT) [15-19] and other technologies have been applied to

analysis of signal. Fourier transformation is the basic of

analysis of time domain and frequency domain for signal,

and is very valid to the analysis of periodic stable signal. But

in nature and engineering areas there is a large number of

non-periodic non stationary signals, and EEG is typical non

periodic signal, so the classic analysis method based on

Fourier transformation cannot accurately reflect the local

time-varying frequency spectral characteristic of signal,

unable to obtain many of the key information.

So a series of new signal time frequency analysis methods

are put forward and developed. The basic idea of time

frequency analysis is to design the joint function of time and

frequency, and at the same time, the density and intensity of

energy of signal at different time and frequency is described.

Before the analysis and comparison on time-frequency

performance of several of methods has been seen, but the

research on the comparison and analysis on Short Time

Fourier transformation, wavelet transformation, HHT and

SST, these four kinds of methods is rare through the

designed signal.

A comprehensive survey of time-frequency decomposition

methods is beyond the scope of this article, but some basic

points about time-frequency transformations can be made

that highlight differences among some of the methods and

also underscore some more general considerations. Perhaps

the most important overarching is that all time-frequency

decomposition methods strike some compromise between

temporal resolution and frequency resolution in resolving

the EEG signals. In general, the larger the time window used

to estimate the complex data for a given time point, the

greater the frequency resolution but the poorer the temporal

resolution. This trade-off between precision in the time

domain vs. the frequency domain is formalized in the

Heisenberg uncertainty principle [20], discussed again in a

later section.

A recent class of time-frequency techniques, referred to as

reassignment methods [21–23], aim to improve the “read

ability” (localization) of time-frequency representations

Paper ID: ART20172894 DOI: 10.21275/ART20172894 2013





[24].The synchrosqueezing transform (SST) [25, 1] belongs

to this class, it is a post-processing technique based on the

continuous wavelet transform that generates highly localized

time-frequency representations of nonlinear and non-

stationary signals. Synchrosqueezing provides a solution that

mitigates the limitations of linear projection based time-

frequency algorithms, such as the short-time Fourier

transform (STFT) and continuous wavelet transforms

(CWT). The synchrosqueezing transform reassigns the

energies of these transforms, such that the resulting energies

of coefficients are concentrated around the instantaneous

frequency curves of the modulated oscillations. As such,

synchrosqueezing is an alternative to the recently introduced

empirical mode decomposition (EMD) algorithm [26]; it

builds upon the EMD, by generating localized time-

frequency representations while at the same time providing a

well understood theoretical basis.

This study first briefly introduces the principles and

characteristics of several methods, short time Fourier

transform, HHT, wavelet transform and SST. So, the time

frequency graphs are made out through simulation signal,

and time frequency performance of four methods is made a

contrast and analysis, to explore the application prospect of

them in processing and analysis of raw EEG signal. This

paper demonstrated the potentiality of the SST in time

frequency representation of EEG signals. Firstly, these

mentioned methods are tested using synthetic signal and

finally, SST and other methods are applied to a real data

sample with high amplitude artifact.

2. Time Frequency Representation Methods

A. Short-Term Fourier Transform

A variant of the fast Fourier transform (FFT), known as the

STFT, or windowed Fourier transform performs a Fourier

transform within a time window that is moved along the

time series in order to characterize changes in power and

phase of EEG signals over time. Typically, a fixed duration

time window is applied to all frequencies. The choice of

time window constrains the frequency binsize (i.e.,

frequency resolution), which is uniform across all

frequencies, and also determines the lowest resolvable

frequency. The uniformity of the characterization of

temporal changes in high-frequency signals requires shorter

time windows than those needed to optimally characterize

low-frequency signals. A more flexible approach in which

window size varies across frequencies to optimize temporal

resolution of different frequencies is therefore desirable. The

STFT for a non-stationary signal s(t) is defined as

)1(2

)].'().([),(

dt

ftettwtsft

where * is the complex conjugate, w(t) is the window

function. The STFT of the signal is the Fourier transform of

the signal multiplied by a window function.The advantage of

STFT is that its physical meaning is clear and there is no

cross term appearing [7-9]. Itis a time frequency analysis

method which application is the most. According to the He

is enbergun certainty principle, the product of time width

and bandwidth of signal should be a constant relevant

to sampling rate. In other words, when time resolution is

needed to improve, the resolution of frequency is often

needed to sacrifice, and vice versa. When the analyzed

signal contains many kinds of types of scale components

with large differences, STFT is powerless. Although STFT

there is the defects such as resolution ratio is not high and so

on, its algorithm is simple, and easy to implement, so in a

long time it is a powerful tool of non-stationary signal

analysis is, and still is widely used.

B. Hilbert-Huang Transform

The Hilbert–Huang transform (HHT) is a way to decompose

a signal into so-called intrinsic mode functions (IMF), and

obtain instantaneous frequency data. In contrast to other

common transforms like the Fourier transform, the HHT is

more like an algorithm (an empirical approach) that can be

applied to a data set, rather than a theoretical tool. It is the

result of the empirical mode decomposition (EMD) and the

Hilbert spectral analysis (HSA). The HHT uses the EMD

method to decompose a signal into so-called intrinsic mode

functions, and uses the HSA method to obtain instantaneous

frequency data. The HHT provides a new method of

analyzing non stationary and nonlinear time series data.

Based on the principle of the empirical mode decomposition

technique [27], the signal ts is represented as

21

trtCts M

M

m

m

where, C1(t), C2(t), . . ., CM(t) are all of the intrinsic mode

functions included in the signals and rM(t) is a negligible

residue. Here, M=total number of intrinsic mode function

components. The completeness of the decomposition is

given by the Eq. (2).

Instantaneous frequency (IF) represents signal’s frequency at

an instance, and is defined as the rate of change of the phase

angle at the instant of the “analytic” version of the signal.

Every IMF is a real valued signal. The discrete Hilbert

transform (HT) denoted by hd [.] is used to compute the

analytic signal for an IMF. HT provides a phase-shift of

±π/2 to all frequency components, whilst leaving the

magnitudes unchanged. Then the analytic version of the

mth

IMF )(ˆ tcm is defined as:

)()()](ˆ[)(ˆ)(

tj

mmdmmmetatcjhtctz

(3)

where ma (t) and )(tm are instantaneous amplitude and

phase respectively of the mth

IMF. The IF of mth

IMF is then

computed by the derivative of the phase )(tm as:

dt

tdtm

)(~

)(

where )(

~tm represents the unwrapped

version of )(tm .The median smoothing filter is used to

tackle the discontinuities of IF computed by discrete time

derivative of the phase vector.

Hilbert spectrum represents the distribution of the signal

energy as a function of time and frequency. It is also

designated as Hilbert amplitude spectrum H(w, t) or simply

Hilbert spectrum (HS). This process first normalizes the IF

vectors of all IMFs between 0 to 0.5. Each IF vector is

multiplied by the scaling factor =0.5/(IFmax-IFmin),


http://en.wikipedia.org/wiki/Signal_processing

http://en.wikipedia.org/wiki/Instantaneous_frequency

http://en.wikipedia.org/wiki/Fourier_transform

http://en.wikipedia.org/wiki/Hilbert_spectral_analysis

http://en.wikipedia.org/wiki/Signal_processing




http://en.wikipedia.org/wiki/Stationary_process

http://en.wikipedia.org/wiki/Nonlinear





where IFmax=Max(f1, f2, …, fm, …., fM) and

IFmin=Min(f1, f2, …, fm, …., fM). The bin spacing of the

HS is 0.5/B, where B is the number of desired frequency

bins selected arbitrarily. Each element H(w, t) is defined as

the weighted sum of the instantaneous amplitudes of all the

IMFs at wth

frequency bin,

)4()()(),(1

twtatHM

m

m m

where the weight factormw (t ) takes 1 if xfm(t) falls within

wth

band, otherwise is 0. After computing the elements over

the frequency bins, H represents the instantaneous signal

spectrum in TF space as a 2D table. The time resolution of H

is equal to the sampling rate and the frequency resolution

can be chosen up to Nyquest limit[15-19, 27].

HHT is an empirical approach, and has been tested and

validated exhaustively but only empirically. In almost all the

cases studied, HHT gives results much sharper than any of

the traditional analysis methods in time-frequency-energy

representation. Additionally, it reveals true physical

meanings in many of the data examined.

C. Wavelet Packet Transform

The wavelet packet transform (WPT) is a generalization of

the wavelet decomposition process that offers a better

performance compared to the ordinary wavelet methods. In

the wavelet analysis, a signal is split into an approximation

and a detail. The approximation is then itself split into a

second-level approximation and detail and the process is

repeated. On the other hand, WPT is applied in both the

detail and the approximation coefficients are divided to get

all nodes for the decomposed levels and generates the full

decomposition tree. A low (l) and high (h) pass filter is

frequently applied to generate a complete subband tree to

some desired depth. The low-pass and high-pass filters are

generated using orthogonal basis functions. The wavelet

packet coefficientsi

kjC , succeeding to the signal ts can be

obtain as,

)5(,,

dttWtsC i

kj

i

kj

where, i is the modulation parameter, j is the dilation

parameter and k is the translation parameter. i = 1, 2, . . ., jL,

and L is the level of decomposition in wavelet packet tree.

By applying WPT on each channel, it produce 2L sub band

wavelet packets, where L is the number of levels .The

structure of WPT decomposition, the lower and the higher

frequency bands are decomposed giving a balanced binary

tree structure. In this present work, five levels is generated

32 subspaces (2L =2

5) and wavelet frequency interval of

each subspace is calculated by

11 2

,2

1L

S

L

S bffbwhere, the frequency factor, b=1, 2,

3, 4, 5, ...............2L,

Sf is the sampling frequency of the

EEG signal. In this studySf =256Hz. ts is the original

signal with the frequency [28].Because wavelet

packets divide the frequency axis into finer intervals than the

DWT, wavelet packets are superior at time-frequency

analysis.

Wavelet packet decomposition algorithm decomposes

gradually not only low frequency band of the signal, but also

the high frequency band of the signal. Furthermore, wavelet

packet decomposition can choose frequency band adaptively

in accordance with the feature of the analyzed signal, and

make a good match with the spectrum of the signal, which

improve time frequency resolution.

D. Synchrosqueezing Transform

The synchrosqueezing transform (SST) is a post processing

technique applied to the continuous wavelet transform in

order to generate localized time-frequency representation of

non-stationary signals. The continuous wavelet transform is

a projection based algorithm that identifies oscillatory

components of interest through a series of time-frequency

filters known as wavelets. The SST was originally

introduced in the context of audio signal analysis and is

shown to be an alternative to EMD.SST aims to decompose

a signal into constituent components with time-varying

harmonic behavior. These signals are assumed to be the

addition of individual time-varying harmonic components

yielding

)6()())(cos()()(1

tttAts k

K

k

k

where )(tAk is the instantaneous amplitude, )(t represents

additive noise, K stands for the maximum number of

components in one signal, and )(tk is the instantaneous

phase of the kth

component. The instantaneous

frequency )(tf k of the kth

component is estimated from the

instantaneous phase as

)7()(2

1)( t

dt

dtf kk

In seismic signals, the number K of harmonics or

components in the signal is infinite. They can appear at

different time slots, with different amplitudes )(tAk ,

instantaneous frequencies )(tf k , and they may be separated

by their spectral bandwidths Δ )(tf k .

The spectral bandwidth defines the spreading around the

central frequency, which in our case is the instantaneous

frequency; for a completed disentangling of concepts. This

magnitude is a constraint for traditional time frequency

representation methods. The STFT and the CWT tend to

smear the energy of the superimposed instantaneous

frequencies around their center frequencies [1]. The

smearing equals the standard deviation around the central

frequency, which is the spectral bandwidth. SST is able to

decompose signals into constituent components with time-

varying oscillatory characteristics. Thus, by using SST we

can recover the amplitude )(tAk and the instantaneous

frequency )(tf k for each component.






From CWT to SST: The CWT of a signal ts is

)8()()(1

),( dta

btts

abasw

where is the complex conjugate of the mother wavelet

and b is the time shift applied to the mother wavelet, which

is also scaled by a. The CWT is the cross correlation of the

signal )(ts with several wavelets that are scaled and

translated versions of the original mother wavelet. The

symbols ),( baws are the coefficients representing a

concentrated time-frequency picture, which is used to extract

the instantaneous frequencies. It is observe that there is a

limit to reduce the smearing effect in the time-frequency

representation using the CWT. This smearing mainly occurs

in the scale dimension a, for constant time offset b show

that if smearing along the time axis can be neglected, then

the instantaneous frequency ),( baws can be computed as

the derivative of the WT at any point ),( ba with respect to

b, for all :0),( baws

)9(),(

),(2),(

b

baW

baW

jbaw s

s

s

The final step in the new time-frequency representation is to

map the information from the time-scale plane to the time-

frequency plane. Every point (b, a) is converted to(b,

),( baws ), and this operation is called synchrosqueezing.

Because a and b are discrete values, we can have a scaling

step kkk aaa 1 for any ka where ),( baWs is

computed. Likewise, when mapping from the time-scale

plane to the time-frequency plan )),(,(),( bawbab inst

the SST ),( bwTs is determined only at the centers l of

the frequency range ]2/,2/[ llwith

:1 ll

)10(),(1

)( .2

3

2),(:

, kk

baa

sls aabaWbT

lkk

The above equation shows that the time-frequency

representation of the signal s(t) is synchrosqueezed

[29]along the frequency (or scale) axis only. The

synchrosqueezing transform reallocates the coefficients of

the continuous wavelet transform to get a concentrated

image over the time frequency plane, from which the

instantaneous frequencies are then extracted; this is an

ultimate goal in EEG signal analysis. The identified

frequencies are used to describe their source EEG and

eventually gain a better understanding of the artifact

detection.

3. Results And Discussion A. Synthetic data

In this section, the different TFR method is tested with a

challenging synthetic signal. A noiseless synthetic signal is

created as the concatenation of the following components

(the IF is in brackets):

];20[);40sin(40)(1 IFtts

];40[);80sin(60)(2 IFtts

];60[);120sin(80)(3 IFtts

(a) The synthetic signals S(t) with three sinusoidal

components. (b) TF representation using Short Term Fourier

Transform.






(c) TF representation using Hilbert Spectrum. (d) TF representation using Hilbert Haung Transform.

(e) TF representation using Wavelet Packet Transform.. (f) TF representation using Synchrosqueezing

Transform.

Figure 1: Synthetic signal S(t) and its TF representation

The synthetic signal s(t) (Figure1a) has three constant

harmonics of 20 Hz (s1(t)) and 40 Hz (s2(t)) from time 0 to

4 s, the 60 Hz component (s3(t )) appears at time 4 s and

vanishes at 6 s. Comparison of Synchrosqueezing with the

STFT, HHT and WPT are illustrated in Figure1.The STFT

is able to identify the three components but with a low

resolution ( Figure 1b), especially when they overlap at 4 s.

Figure 1c) shows the instantaneous frequencies for each

component using HHT. It looks better time resolution than

STFT but lower frequency resolution for wide frequency

bandwidth. Figure 1e) shows the instantaneous frequencies

for each component using decimated WPT. The WPT is able

to identify the three components but with a low resolution, it

is good for nearest frequency resolution. On the other hand,

the SST (Figure 1f) is able to perfectly delineate each

individual component and to resolve the instantaneous

frequencies close to the theoretical value, which are

presented good time and frequency resolution. For

comparison purposes, we include the HHT result, because

the SST is an extension of the CWT and EMD. The

instantaneous frequencies obtained as the derivative of each

one of the independent components. In the SST shows a

sharper representation of the instantaneous frequencies.

Figure1.shows the STFT, HHT, WPT and SST time-

frequency representations. Four methods all can distinguish

the change of main frequency. From Figure1, spectrum

graph of short time Furious transformation it can be seen

that, although this figure can distinguish the moment of three

main frequency components and mutation occurrence, the

resolution is not high. According to the Heisenberg

uncertainty principle, the product of time width and

bandwidth of signal should be a constant relevant to

sampling rate. In other words, when time resolution is

needed to improve, the resolution of frequency is often

needed to sacrifice, and vice versa. For EEG signal, when

the frequency resolution is required, the time window length

is likely to appear too large, and at this time FFT may be

difficult to meet the requirement. The treatment effect is not

satisfactory for non-stationary nonlinear signal such as EEG.

Figure1(d) is the HHT spectrum. It can be seen from the

figure that processing effect of HHT on nonlinear unstable

signal has a unique advantage, because this method does not

exist the steps of partition and translation of windows when

using, adopting that separately making analysis for the short

time series. Therefore, it makes a good balance between the

requirements of time resolution and frequency resolution,

that is to say, as long as it meets the Shannon theorem (i.e.,

sampling law), this method can improve time domain

resolution as much as possible under the situation that

without sacrificing frequency domain resolution. Despite the

high-amplitude noise, the resonance frequencies as well as

their variations are all clearly visible on the SST

representation (Figure1f). The SST is able to map smooth






and sharp changes in the frequency lines. Compared with the

STFT, the SST brings out the resonance frequencies more

sharply, improving significantly the frequency resolution.

The SST is then able to distinguish between the different

lines constituting the resonance frequency at 2, 4 and 8 Hz

while the STFT cannot. Last but not least, the SST

determines the IFs at all times. Therefore, the time

resolution of this method is not limited by the size of any

window.

B. Application to real EEG data

Dataset description: In this section, the real EEG data used to evaluate the TFR

method is collected from well-known publicly available real

EEG data set (downloaded from

http://www.commsp.ee.ic.ac.uk/~mandic/EEG-256Hz.zip).

The data was recorded from 8 electrodes for 30 seconds and

sampled at 256Hz. The labels for the recorded electrodes are

provided in each mat file. The ground electrode was placed

at position Cz, according to the 10-20 system. The electrode

positions used were Fp1, Fp2, C3, C4, O1, O2, vEOG,

hEOG and correspond respectively to the columns of the

data matrix. For instance data(:, 1) gives the recordings

corresponding to Fp1.This data set also contains EOG

artifacts from blink of the eyes. In addition, the data set was

sampled at 256 Hz and notch filtered at 50 Hz. It shows the

real EEG signals, the EOG artifacts were present on all six

EEG channels, while the artifacts are much stronger on the

frontal lobe electrodes (Fp1, Fp2) and highly non-stationary

(its amplitude differs between successive eye movements).

Unlike the “artificially” contaminated EEG recordings, there

is no ground truth “pure” EEG (pre-contaminated EEG).

a)Time domain representation of raw EEG signal. (b) Short Term Fourier Transform TFR for raw EEG

signal.

(c) Hilbert Spectrum for raw EEG signal. (d) TFR using raw EEG for HHT.






e) TFR using raw EEG for WPT. f) Synchrosqueezing TF representation using raw EEG

signal. Figure 2: Time-frequency analysis of raw EEG signal. Upper plot shows the STFT and the lower plot the SST. The

SST is able to delineate the spectral components some of them were missing in the STFT representation.

Experimental results

In this section we apply the different time frequency

representation method as like as SST, HHT, WT and SST to

a real dataset. Figure 2. illustrared different time frequency

representation method using raw EEG. From the TFR

representation it is visualized the presence of artifact in EEG

signal. Typically 0.5 to 100 µV are the range of EEG signal

and it lies between 0 to 50 Hz. Generally the ocular artifacts

are occur in the range between 0 to 8 or 10 hz, and muscle

artifacts present over 20 Hz. The spectral analysis of wide-

sense stationary signals using the Fourier transform is well-

established. For nonstationary signals, there exist local

Fourier methods such as the short-time Fourier transforms

(STFT). Because wavelets are localized in time and

frequency, it is possible to use wavelet-based counterparts to

the STFT for the time-frequency analysis of nonstationary

signals. For example, it is possible to construct the

scalogram based on the continuous wavelet transform

(CWT). However, a potential drawback of using the CWT is

that it is computationally expensive. The discrete wavelet

transform (DWT) permits a time-frequency decomposition

of the input signal, but the degree of frequency resolution in

the DWT is typically considered too coarse for practical

time-frequency analysis. As a compromise between the

DWT- and CWT-based techniques, wavelet packets provide

a computationally-efficient alternative with sufficient

frequency resolution. a time-frequency analysis of EEG

signal using wavelet packets is presented in this section.

In the STFT a Hamming window of length 256 and 50%

overlap is used. The STFT is able to recognize the three

components but with a poor resolution.In this present work,

in WPT the frequency bands corresponding to five

decomposition levels for Daubechies 4 (db4) mother wavelet

which is chosen for this filter. Hilbert spectral analysis

(HSA) is a method for examining each IMF's instantaneous

frequency as functions of time. The final result is a

frequency-time distribution of signal amplitude (or energy),

designated as the Hilbert spectrum, which permits the

identification of localized features. The individual IMFs are

completely disjoint at any temporal position. The overall

effect of IF of all IMFs is used in time-frequency (TF)

representation of the time domain signal. For the SST a

bump wavelet is used with a ratio central frequency to

bandwidth of 50. The discretization of the scales of CWT is

64. The SST produces a sharper time-frequency

representation showing frequency components that were

hidden in the STFT representation. From Figure2, it is clear

that the three methods (STFT, HHT and SST) clearly shown

the EEG signal lies below the 20 Hz except WPT. The TFR

of WPT shows the EEG signal lies all over the frequency 0

to 128 Hz but below 20 Hz it exhibits high energy. The high

energy indicate the artifacts of EEG signal and obviously the

artifact is ocular artifact which is found in similarity in

Figure2(a).From Figure 2 (a), it is seen that the raw EEG is

mixed with EOG( eye blink) artifact. So, from above TFR, it

is clear that the frequency localization of WPT is good for

real EEG than SST but the time and frequency resolution is

better of SST than other three methods namely STFT, HHT

and WPT.

4. Conclusions

The examples given in this text lead to the conclusion that

among the tested TFRs, SST are really valuable tools in

analyzing the frequency content of EEG. The proposed

method is computationally fast and is suitable for real-time

BCI applications. To evaluate the TFR, a comparison with

short-time Fourier transform (STFT), Hilbert–Huang

transform (HHT) and wavelet packet transform (WPT)for

both synthesized and real EEG data is performed in this

paper. The popular methods of STFT has limitations in

representing close frequencies and dealing with fast varying

instantaneous frequencies and this is often the nature of EEG

signals. HHT spectrum displays the distribution of signal

energy in time frequency domain, and can help more clearly

understand the distribution situation of low and high

frequency part in signal. Moreover, HHT method structures

basis function from the signal itself, directly reflects the

characteristic of signal itself, and eliminate the generated

virtual volume due to the mismatch of base function and

signal in transformation process. so the obtained HHT

spectrum can not only locate the position of frequency

mutation point, but also can accurately distinguish two main

frequency components The time frequency resolution of

wavelet transformation are both very good, for the smaller

frequency component, the time point of frequency hopping


http://en.wikipedia.org/wiki/Hilbert_spectral_analysis




http://en.wikipedia.org/wiki/Hilbert_spectrum





is described not enough accurately. The synchrosqueezing

transform (SST) is a promising tool to track these resonant

frequencies and provide a detailed time-frequency

representation. The synchrosqueezing transform to EEG

signals and also show its superior precision, in both time and

frequency, at identifying the components of complicated

oscillatory signals. Synchrosqueezing can be used to analyze

spectrally and decompose a wide variety of signals with high

precision in time and frequency.

5. Acknowledgement

This research work is supported by the Information and

Communication Technology (ICT) division of the ministry

of Post, Telecommunication and Information Technology,

Bangladesh.

6. Conflicts of Interest

The authors declare that there is no conflict of interests

regarding the publication of this paper.

References

[1] I. Daubechies, and S. Maes, “A nonlinear squeezing of

the continuous wavelet transform based on auditory

nerve models”, Wavelets in Medicine and Biology,

CRC Press, pp.527–546, 1996.

[2] Wu, H.-T., P. Flandrin, and I. Daubechies, “One or

Two Frequencies? The Synchrosqueezing Answers”,

Advances in Adaptive Data Analysis (AADA), vol.03,

pp.29–39, 2011.

[3] K. Morikawa, A. Matsumoto, S. Patki, B. Grundlehner,

A.Verwegen, J. Xu, S. Mitra and J.Penders, “Compact

Wireless EEG System with Active Electrodes for Daily

Healthcare Monitoring”, IEEE International

Conference on Consumer Electronics (ICCE), 204-

205, 2013.

[4] SN. Tang, F.C. Jan, H.W. Cheng, C.K. Lin, G. Z. Wu,

“Multimode Memory-Based FFT Processor for

Wireless Display FD-OCT Medical Systems”, IEEE

Transactions on Circuits and Systems I:Regular

Papersvol.61, no.12, pp.3394 – 3406, 2014.

[5] J. Han, L. Zhang, G. Leus, “Partial FFT Demodulation

for MIMO-OFDM Over Time-Varying Underwater

Acoustic Channels”, IEEE Signal Processing Letters,

vol.23 no.2, pp.282 – 286, 2016.

[6] T. Yang, H. Pen, Z. Wang, C. S. Chang, “Feature

Knowledge Based Fault Detection of Induction Motors

Through the Analysis of Stator Current Data”, IEEE

Transactions on Instrumentation and Measurement,

vol.65, no. 3, pp.549 – 558, 2016.

[7] W. Liu, X. Zhang, “Signal modulation characteristic

analysis based on SFFT-Haar algorithm”, IET

International Radar Conference, pp.1 – 4, 2013

[8] B. Kim, S.H. Kong, S. Kim, “Low Computational

Enhancement of STFT-Based Parameter Estimation”,

IEEE Journal of Selected Topics in Signal Processing,

vol.9, no.8, pp.1610 - 1619, 2015.

[9] K. Jaganathan, Y. C. Eldar, B. Hassibi, “STFT Phase

Retrieval: Uniqueness Guarantees and Recovery

Algorithms”, IEEE Journal of Selected Topics in

Signal Processing, vol. 10, no.4, pp .770 -781, 2016.

[10] R. Mothi, M. Karthikeyan, “A wavelet packet and

fuzzy based digital image watermarking”, IEEE

International Conference on Computational

Intelligence and Computing Research (ICCIC), pp.1 –

5, 2013.

[11] J.S Pan, and L. Yue, “A ridge extraction algorithm

based on partial differential equations of the wavelet

transform”, IEEE Symposium on Computational

Intelligence for Multimedia, Signal and Vision

Processing (CIMSIVP), Orlando, FL, pp.1 – 5, 2014.

[12] S.A.R. Naqvi, I. Touqir, and S.A. Raza, “Adaptive

geometric wavelet transform based two dimensional

data compression”, 7th IEEE GCC Conference and

Exhibition (GCC), Doha, pp.583 – 588, 2013.

[13] G. Serbes, N. Aydin, and H.O. Gulcur, “Directional

dual-tree complex wavelet packet transform”, 35th

Annual International Conference of the IEEE,

Engineering in Medicine and Biology Society

(EMBC), Osaka, pp.3046-3049, 2013.

[14] S. Bharkad, and M. Kokare, “Fingerprint matching

using discreet wavelet packet transform”, IEEE 3rd

International Advance Computing Conference (IACC),

Ghaziabad, pp.1183-1188, 2013.

[15] K. Rai, V. Bajaj, “A. Kumar, Hilbert-Huang transform

based classification of sleep and wake EEG signals

using fuzzy c-means algorithm”, International

Conference on Communications and Signal Processing

(ICCSP), IEEE, Melmaruvathur, pp. 0460 – 0464,

2015.

[16] Y. Wang, C. Chen, H. He, “Large Eddy Simulation

and Hilbert Huang Transform for fluctuation pressure

of high speed train”, IEEE International

Instrumentation and Measurement Technology

Conference (I2MTC), Pisa, pp. 284 – 288, 2015.

[17] R.K.Chaurasiya, K. Jain, S. G., Manisha, “Epileptic

seizure detection using HHT and SVM”, International

Conference on Electrical, Electronics, Signals,

Communication and Optimization (EESCO),

Visakhapatnam, pp. 1 – 6, 2015.

[18] K. Y. Lin, D. Y. Chen, W. J. Tsai, “Face-Based Heart

Rate Signal Decomposition and Evaluation Using

Multiple Linear Regression”, IEEE Sensors Journal,

vol.16, no. 5, pp. 1351 – 1360, 2016.

[19] P.Y.Chen, Y.C. Lai, J.Y. Zheng, “Hardware Design

and Implementation for Empirical Mode

Decomposition”, IEEE Transactions on Industrial

Electronics, PP ( 99 ): 1.2016.

[20] G.B.Folland, A.Sitaram“The uncertainty principle: a

mathematicalsurvey”, J Fourier Anal Appl.Vol.3,

pp.207–233, 1997.

[21] K. Kodera, R.Gendrin, C.Villedary, ”Analysis of time-

varying signals with small BT values”, IEEE Trans

Acoust. Speech Signal Process, vol.26, no.1, pp.64–76,

1978.

[22] F.Auger, P.Flandrin, “Improving there adability of

time-frequency and time scale representations by their

assignment method”, IEEE Trans. Signal Process,

vol.43, no.5, pp.1068–1089, 1995.

[23] F.Auger, P. Flandrin, Y.-T. Lin, S. Mc Laughlin, S.

Meignen, T. Oberlin, H.-T.Wu, “Time frequency

reassignment and synchrosqueezing: an overview”,






IEEE Signal Process. Mag, vol.30, no.6, pp.32–41,

2013.

[24] R. Carmona, W.-L.Hwang, B.Torrésani, Practica,

“Time-Frequency Analysis, Academic Press, 1998.

[25] I. Daubechies, J.Lu, H.-T.Wu, “Synchrosqueezed

wavelet transforms: an empirical mode decomposition-

like tool”, Appl. Comput. Harmo- nic Anal. Vol.30,

no.2, pp.243–261, 2011.

[26] N. Huang, Z. Shen, S. Long, M. Wu, H. Shih, Q.

Zheng, N. Yen, C.Tung, H. Liu, “The empirical mode

decomposition and the Hilbert spectrum for nonlinear

random stationary time series analysis”, Proc. R. Soc.

A 454, pp.903–995, 1998.

[27] M.K.I. Molla, K. Hirose, and N.Minematsu1,

“Separation of Mixed Audio Signals by Source

Localization and Binary Masking with Hilbert

Spectrum”, Springer-Verlag Berlin Heidelberg, pp.

641 – 648, 2006.

[28] Y.-J.Xu, S.-D. Xiu, “A new and effective method of

bearing fault diagnosis using wavelet packet transform

combined with support vector machine,” Journal of

Computers, vol. 6, no. 11, Nov. 2011.

[29] R. H. Herrera, J. Han, and M. van der Baan,

“Applications of the synchrosqueezing transform in

seismic time-frequency analysis”, GEOPHYSICS,

vol.79, no.3, pp.v55-v64, May-June, 2014.


time-frequency analysis of eeg signal processing for

Documents